\begin{table}[htbp!] \footnotesize \centering \begin{threeparttable} \caption{Determinants of nudge adoptions} \begin{tabular} {l c c c c c c c c} \toprule & \multicolumn{6}{c}{OLS} & Logit & ML \\ \cmidrule(lr){2-7} \cmidrule(lr){8-8} \cmidrule(lr){9-9} Dep. var.: Nudge adopted (0/1) & (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) \\ \hline 
Max $ t\geq1.96$ & 0.02 & & & -0.03 & -0.16 & -0.24 & -0.20 & -0.69 \\
& (0.13) & & & (0.08) & (0.10) & (0.11) & (0.59) & (0.51) \\
Max treatment effect (10pp.) & 0.06 & & & 0.10 & 0.14 & 0.23 & 0.78 & \\
& (0.12) & & & (0.07) & (0.09) & (0.13) & (0.52) & \\
City staff retained & & 0.13 & & 0.07 & 0.00 & -0.06 & 0.61 & -0.63 \\
& & (0.08) & & (0.08) & (0.11) & (0.13) & (0.53) & (0.52) \\
Above-median city population & & 0.07 & & 0.06 & & & 0.26 & 0.27 \\
& & (0.12) & & (0.08) & & & (0.68) & (0.62) \\
What Works Cities certified & & 0.06 & & 0.14 & & & 1.10 & -0.07 \\
& & (0.12) & & (0.11) & & & (0.86) & (0.61) \\
Communication pre-existed & & & 0.53 & 0.52 & 0.59 & 0.60 & 2.91 & 2.58 \\
& & & (0.13) & (0.13) & (0.14) & (0.15) & (0.67) & (0.79) \\ \multicolumn{9}{l}{\textit{Mechanism}} \\
\hspace{1em}Simplification \& information & & & 0.01 & 0.03 & 0.06 & 0.21 & 0.21 & -0.46 \\
& & & (0.10) & (0.10) & (0.13) & (0.14) & (0.80) & (0.81) \\
\hspace{1em}Personal motivation & & & -0.13 & -0.12 & -0.00 & 0.02 & -0.93 & -1.66 \\
& & & (0.11) & (0.12) & (0.14) & (0.10) & (0.89) & (0.77) \\
\hspace{1em}Social cues & & & -0.06 & -0.08 & 0.06 & 0.08 & -0.66 & -0.91 \\
& & & (0.08) & (0.08) & (0.06) & (0.08) & (0.58) & (0.37) \\
Control take-up (10\%) & & & & & & 0.02 & & \\
& & & & & & (0.03) & & \\
Uses online mediums & & & & & & 0.32 & & \\
& & & & & & (0.12) & & \\
Years since trial & & & & & & -0.00 & & \\
& & & & & & (0.06) & & \\
City dept. in charge of implementing & & & & & & 0.29 & & \\
& & & & & & (0.19) & & \\
Senior city staff on trial (Director/Chief) & & & & & & 0.07 & & \\
& & & & & & (0.14) & & \\ \multicolumn{9}{l}{\textit{Prior parameters}} \\
\hspace{1em}$\mu_0$ & & & & & & & & 0.40 \\
& & & & & & & & (1.09) \\
\hspace{1em}$\sigma_0$ & & & & & & & & 0.23 \\
& & & & & & & & (0.08) \\
Constant & 0.25 & 0.12 & 0.22 & 0.05 & 0.07 & -0.38 & -2.71 & \\
& (0.07) & (0.12) & (0.10) & (0.15) & (0.11) & (0.46) & (1.19) & \\ \hline
Average adoption rate & 0.27 & 0.27 & 0.27 & 0.27 & 0.27 & 0.27 & 0.27 & 0.27 \\
City fixed effects & & & & & $\checkmark$ & $\checkmark$ & & \\
Policy area fixed effects & & & & & & $\checkmark$ & & \\
Number of trials & 73 & 73 & 73 & 73 & 73 & 73 & 73 & 73 \\
Number of cities & 30 & 30 & 30 & 30 & 30 & 30 & 30 & 30 \\
(Pseudo-)$ R^2$ & 0.01 & 0.03 & 0.34 & 0.38 & 0.69 & 0.79 & 0.33 & 0.25 \\
\bottomrule \end{tabular} \label{tab:reg} \begin{tablenotes} \scriptsize \item Standard errors clustered by city are shown in parentheses. Policy area fixed effects includes a dummy each of the policy areas (Community engagement; Environment; Health; Registration \& regulation compliance; Revenue collection \& debt repayment; Take-up of benefits and programs; and Workforce \& education). 3 trials are missing the data on the seniority of the city staff member working on the trial (Column 6); these trials are included with an indicator for missing. Column 8 estimates the model from Section 3 via maximum likelihood. The model specifies the distribution of the policy-maker's prior on the percentage point effectiveness of the nudge as $ N(\mu_{0},\sigma_{0}^2).$ The policy-maker updates after observing the treatment effect of the nudge from the trial. The weight placed on the signal is $ \sigma_{0}^2/(\sigma_{s}^2 + \sigma_{0}^2),$ where $ \sigma_{s}^2$ is the sampling variance or the square of the standard error, and the weight on the prior is $ \sigma_{s}^2/(\sigma_{s}^2 + \sigma_{0}^2).$ The average sampling variance is 1.51, which gives a weight on the signal of 0.03, and the median is 0.35, which provides a signal weight of 0.13. \end{tablenotes} \end{threeparttable} \end{table}
